An exact Gibbs sampler for the Markov-modulated Poisson process

Authors


Chris Sherlock, Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster, LA1 4YF, UK.
E-mail: c.sherlock@lancs.ac.uk

Abstract

Summary.  A Markov-modulated Poisson process is a Poisson process whose intensity varies according to a Markov process. We present a novel technique for simulating from the exact distribution of a continuous time Markov chain over an interval given the start and end states and the infinitesimal generator, and we use this to create a Gibbs sampler which samples from the exact distribution of the hidden Markov chain in a Markov-modulated Poisson process. We apply the Gibbs sampler to modelling the occurrence of a rare DNA motif (the Chi site) and to inferring regions of the genome with evidence of high or low intensities for occurrences of this site.

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